A bstract In this paper, we introduce a new quantity called SVD entanglement entropy. This
is a generalization of entanglement entropy in that it depends on two different states, as in …

Bayes' rule, P (B| A) P (A)= P (A| B) P (B), is one of the simplest yet most profound,
ubiquitous, and far-reaching results of classical probability theory, with applications in any …

We propose a category-theoretic definition of retrodiction and use it to exhibit a time-reversal
symmetry for all quantum channels. We do this by introducing retrodiction families and …

The quantum no-broadcasting theorem states that it is impossible to produce perfect copies
of an arbitrary quantum state, even if the copies are allowed to be correlated. Here we show …

The conventional framework of quantum theory treats space and time in vastly different ways
by representing temporal correlations via quantum channels and spatial correlations via …

We consider how to tell the time-ordering associated with measurement data from quantum
experiments at two times and any number of qubits. We define an arrow of time inference …

We consider the relation between three different approaches to defining quantum states
across several times and locations: the pseudo-density matrix (PDM), the process matrix …

While in relativity theory space evolves over time into a single entity known as spacetime,
quantum theory lacks a standard notion of how to encapsulate the dynamical evolution of a …

The measurement statistics for spatial and temporal quantum processes are produced
through distinct mechanisms. Measurements that are space‐like separated exhibit non …

We consider the quantum version of inferring the causal relation between events. There has
been recent progress towards identifying minimal interventions and observations needed …